{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T09:50:08Z","timestamp":1762509008603,"version":"3.37.3"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T00:00:00Z","timestamp":1685145600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T00:00:00Z","timestamp":1685145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2017\/17840-2","2017\/18308-2","2018\/24293-0"],"award-info":[{"award-number":["2017\/17840-2","2017\/18308-2","2018\/24293-0"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["301888\/2017-5","303427\/2018-3","404656\/2018-8","E-26\/010.001247\/2016"],"award-info":[{"award-number":["301888\/2017-5","303427\/2018-3","404656\/2018-8","E-26\/010.001247\/2016"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["1201982"],"award-info":[{"award-number":["1201982"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100020884","name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","doi-asserted-by":"crossref","award":["170001"],"award-info":[{"award-number":["170001"]}],"id":[{"id":"10.13039\/501100020884","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["E-26\/010.001247\/2016"],"award-info":[{"award-number":["E-26\/010.001247\/2016"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2018\/24293-0","2013\/07375-0","306988\/2021-6"],"award-info":[{"award-number":["2018\/24293-0","2013\/07375-0","306988\/2021-6"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2024,5]]},"DOI":"10.1007\/s10107-023-01970-4","type":"journal-article","created":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T14:01:25Z","timestamp":1685196085000},"page":"1-32","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Weak notions of nondegeneracy in nonlinear semidefinite programming"],"prefix":"10.1007","volume":"205","author":[{"given":"Roberto","family":"Andreani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gabriel","family":"Haeser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2851-8285","authenticated-orcid":false,"given":"Leonardo M.","family":"Mito","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H\u00e9ctor","family":"Ram\u00edrez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,5,27]]},"reference":[{"issue":"1\u20132","key":"1970_CR1","first-page":"5","volume":"111","author":"R Andreani","year":"2008","unstructured":"Andreani, R., Birgin, E.G., Mart\u00ednez, J.M., Schuverdt, M.L.: Augmented lagragrian methods under the constant positive linear dependence constraint qualification. Math. Program. 111(1\u20132), 5\u201332 (2008)","journal-title":"Math. Program."},{"key":"1970_CR2","doi-asserted-by":"publisher","unstructured":"Andreani, R., Fukuda, E. H., Haeser, G., Ram\u00edrez C. H., Santos, D. O., Silva, P. J. S., Silveira, T. P.: Erratum to: new constraint qualifications and optimality conditions for second order cone programs. To appear in Set Valued Variation. Anal. (2021). https:\/\/doi.org\/10.1007\/s11228-021-00573-5.","DOI":"10.1007\/s11228-021-00573-5."},{"key":"1970_CR3","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1080\/02331930903578700","volume":"60","author":"R Andreani","year":"2011","unstructured":"Andreani, R., Haeser, G., Mart\u00ednez, J.M.: On sequential optimality conditions for smooth constrained optimization. Optimization 60, 627\u2013641 (2011)","journal-title":"Optimization"},{"key":"1970_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-021-01737-w","author":"R Andreani","year":"2021","unstructured":"Andreani, R., Haeser, G., Mito, L.M., Ram\u00edrez, H., Santos, D.O., Silveira, T.P.: Naive constant rank-type constraint qualifications for multifold second-order cone programming and semidefinite programming. Opt. Lett. (2021). https:\/\/doi.org\/10.1007\/s11590-021-01737-w","journal-title":"Opt. Lett."},{"key":"1970_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-021-01212-8","author":"R Andreani","year":"2021","unstructured":"Andreani, R., Haeser, G., Mito, L.M., Ramos, A., Secchin, L.D.: On the best achievable quality of limit points of augmented Lagrangian schemes. Numer. Algorithms (2021). https:\/\/doi.org\/10.1007\/s11075-021-01212-8","journal-title":"Numer. Algorithms"},{"key":"1970_CR6","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1137\/110843939","volume":"22","author":"R Andreani","year":"2012","unstructured":"Andreani, R., Haeser, G., Schuverdt, M.L., Silva, P.J.S.: Two new weak constraint qualifications and applications. SIAM J. Opt. 22, 1109\u20131135 (2012)","journal-title":"SIAM J. Opt."},{"key":"1970_CR7","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s10107-011-0456-0","volume":"135","author":"R Andreani","year":"2012","unstructured":"Andreani, R., Haeser, G., Schuverdt, M.L., Silva, P.J.S.: A relaxed constant positive linear dependence constraint qualification and applications. Math. Program. 135, 255\u2013273 (2012)","journal-title":"Math. Program."},{"issue":"1\u20132","key":"1970_CR8","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s10107-018-1354-5","volume":"180","author":"R Andreani","year":"2020","unstructured":"Andreani, R., Haeser, G., Viana, D.S.: Optimality conditions and global convergence for nonlinear semidefinite programming. Math. Program. 180(1\u20132), 203\u2013235 (2020)","journal-title":"Math. Program."},{"key":"1970_CR9","doi-asserted-by":"crossref","unstructured":"Anjos, M. F., Lassere, J. B.: (eds.). Handbook on semidefinite, conic and polynomial optimization. International Series in Operations Research and Management Science. Springer US. New York (2012)","DOI":"10.1007\/978-1-4614-0769-0"},{"key":"1970_CR10","doi-asserted-by":"crossref","unstructured":"Auslender, A., Ram\u00edrez, H.: Penalty and barrier methods for convex semidefinite programming. Math. Methods Oper. Res., 63, Article number: 195 (2006)","DOI":"10.1007\/s00186-005-0054-0"},{"key":"1970_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1394-9","volume-title":"Pertubation Analysis of Optimization Problems","author":"JF Bonnans","year":"2000","unstructured":"Bonnans, J.F., Shapiro, A.: Pertubation Analysis of Optimization Problems. Springer-Verlag, Berlin (2000)"},{"issue":"1\u20132","key":"1970_CR12","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s10107-015-0915-0","volume":"158","author":"D Dorsch","year":"2016","unstructured":"Dorsch, D., G\u00f3mez, W., Shikhman, V.: Sufficient optimality conditions hold for almost all nonlinear semidefinite programs. Math. Program. 158(1\u20132), 77\u201397 (2016)","journal-title":"Math. Program."},{"key":"1970_CR13","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/PL00011370","volume":"88","author":"A Forsgren","year":"2000","unstructured":"Forsgren, A.: Optimality conditions for nonconvex semidefinite programming. Math. Program. 88, 105\u2013128 (2000)","journal-title":"Math. Program."},{"issue":"2","key":"1970_CR14","doi-asserted-by":"publisher","first-page":"1041","DOI":"10.1137\/120887035","volume":"23","author":"P Fusek","year":"2013","unstructured":"Fusek, P.: On metric regularity for weakly almost piecewise smooth functions and some applications in nonlinear semidefinite programming. SIAM J. Opt. 23(2), 1041\u20131061 (2013)","journal-title":"SIAM J. Opt."},{"key":"1970_CR15","doi-asserted-by":"crossref","unstructured":"Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)","DOI":"10.1017\/CBO9780511810817"},{"key":"1970_CR16","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/BFb0121215","volume":"21","author":"R Janin","year":"1984","unstructured":"Janin, R.: Direction derivative of the marginal function in nonlinear programming. Math. Program. Stud. 21, 127\u2013138 (1984)","journal-title":"Math. Program. Stud."},{"issue":"3","key":"1970_CR17","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/s00186-013-0429-6","volume":"77","author":"D Klatte","year":"2013","unstructured":"Klatte, D., Kummer, B.: Aubin property and uniqueness of solutions in cone constrained optimization. Math. Methods Oper. Res. 77(3), 291\u2013304 (2013)","journal-title":"Math. Methods Oper. Res."},{"issue":"4","key":"1970_CR18","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1080\/02331930902971377","volume":"60","author":"L Minchenko","year":"2011","unstructured":"Minchenko, L., Stakhovski, S.: On relaxed constant rank regularity condition in mathematical programming. Optimization 60(4), 429\u2013440 (2011)","journal-title":"Optimization"},{"issue":"1","key":"1970_CR19","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1287\/moor.2014.0669","volume":"40","author":"BS Mordukhovich","year":"2015","unstructured":"Mordukhovich, B.S., Nghia, T.T.A., Rockafellar, R.T.: Full stability in finite-dimensional optimization. Math. Oper. Res. 40(1), 226\u2013252 (2015)","journal-title":"Math. Oper. Res."},{"key":"1970_CR20","doi-asserted-by":"crossref","unstructured":"Mordukhovich, B.S., Outrata, J. V., Ram\u00edrez, H.: Graphical derivatives and stability analysis for parameterized equilibria with conic constraints. Set Valued Anal. Appl., pp. 1\u201318 (2015)","DOI":"10.1007\/s11228-015-0328-5"},{"issue":"1","key":"1970_CR21","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1137\/120903221","volume":"25","author":"BS Mordukhovich","year":"2015","unstructured":"Mordukhovich, B.S., Outrata, J.V., Ram\u00edrez, H.: Second-order variational analysis in conic programming with applications to optimality and stability. SIAM J. Opt. 25(1), 76\u2013101 (2015)","journal-title":"SIAM J. Opt."},{"key":"1970_CR22","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1007\/978-1-4614-7621-4_28","volume-title":"Computational and Analytical Mathematics","author":"G Pataki","year":"2013","unstructured":"Pataki, G.: Strong duality in conic linear programming: facial reduction and extended duals. In: Bailey, D., et al. (eds.) Computational and Analytical Mathematics, vol. 50, pp. 613\u2013634. Springer Proceedings in Mathematics and Statistics, New York, NY (2013)"},{"key":"1970_CR23","doi-asserted-by":"publisher","first-page":"963","DOI":"10.1137\/S1052623497326629","volume":"10","author":"L Qi","year":"2000","unstructured":"Qi, L., Wei, Z.: On the constant positive linear dependence conditions and its application to SQP methods. SIAM J. Opt. 10, 963\u2013981 (2000)","journal-title":"SIAM J. Opt."},{"issue":"4","key":"1970_CR24","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1137\/0130053","volume":"30","author":"SM Robinson","year":"1976","unstructured":"Robinson, S.M.: First-order conditions for general nonlinear optimization. SIAM J. Appl. Math. 30(4), 597\u2013610 (1976)","journal-title":"SIAM J. Appl. Math."},{"issue":"2","key":"1970_CR25","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/BF02614439","volume":"77","author":"A Shapiro","year":"1997","unstructured":"Shapiro, A.: First and second order analysis of nonlinear semidefinite programs. Math. Program. Ser. B 77(2), 301\u2013320 (1997)","journal-title":"Math. Program. Ser. B"},{"issue":"2","key":"1970_CR26","doi-asserted-by":"publisher","first-page":"508","DOI":"10.1137\/S1052623495279785","volume":"7","author":"A Shapiro","year":"1997","unstructured":"Shapiro, A.: On uniqueness of Lagrange multipliers in optimization problems subject to cone constraints. SIAM J. Opt. 7(2), 508\u2013518 (1997)","journal-title":"SIAM J. Opt."},{"issue":"3","key":"1970_CR27","doi-asserted-by":"publisher","first-page":"552","DOI":"10.1137\/0805028","volume":"5","author":"A Shapiro","year":"1995","unstructured":"Shapiro, A., Fan, M.K.H.: On Eigenvalue optimization. SIAM J. Opt. 5(3), 552\u2013569 (1995)","journal-title":"SIAM J. Opt."},{"issue":"4","key":"1970_CR28","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1287\/moor.1060.0195","volume":"31","author":"D Sun","year":"2006","unstructured":"Sun, D.: The strong second-order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications. Math. Oper. Res. 31(4), 761\u2013776 (2006)","journal-title":"Math. Oper. Res."},{"issue":"1","key":"1970_CR29","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.orl.2012.11.009","volume":"41","author":"G Wachsmuth","year":"2013","unstructured":"Wachsmuth, G.: On LICQ and the uniqueness of Lagrange multipliers. Oper. Res. Lett. 41(1), 78\u201380 (2013)","journal-title":"Oper. Res. Lett."},{"key":"1970_CR30","doi-asserted-by":"crossref","unstructured":"Wolkowicz, H., Saigal, R. L.: Vandenberghe (eds.) Handbook of Semidefinite Programming: Theory, Algorithms, an Applications. In: International Series in Operations Research and Management Science. Springer US. New York, (2000)","DOI":"10.1007\/978-1-4615-4381-7"},{"issue":"1","key":"1970_CR31","first-page":"24","volume":"58","author":"H Yamashita","year":"2015","unstructured":"Yamashita, H., Yabe, H.: A survey of numerical methods for nonlinear semidefinite programming. J. Oper. Res. Soc. Japan 58(1), 24\u201360 (2015)","journal-title":"J. Oper. Res. Soc. Japan"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-023-01970-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10107-023-01970-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-023-01970-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,6]],"date-time":"2024-04-06T14:12:43Z","timestamp":1712412763000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10107-023-01970-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,27]]},"references-count":31,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2024,5]]}},"alternative-id":["1970"],"URL":"https:\/\/doi.org\/10.1007\/s10107-023-01970-4","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"type":"print","value":"0025-5610"},{"type":"electronic","value":"1436-4646"}],"subject":[],"published":{"date-parts":[[2023,5,27]]},"assertion":[{"value":"29 December 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 April 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 May 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}